Example of Fully Nested ANOVA

A manufacturing engineer wants to understand the sources of variability in the manufacture of glass jars. The engineer's company manufactures the glass jars at four locations. Four operators measure furnace temperatures in three batches over four shifts from the four locations.

The operators at each plant are different, so the operator factor is nested in the plant factor. While each shift number represents the same part of the workday, the shifts that each operator works at the same plant are different. Thus, shift is nested in operator. Also, the batch of material that the operators use changes each shift. Thus, batch is nested in shift. Because of the nesting pattern, the engineer uses fully nested ANOVA so that the model specification in Minitab is easier.

  1. Open the sample data, FurnaceTemperature.MTW.
  2. Choose Stat > ANOVA > Fully Nested ANOVA.
  3. In Responses, enter Temp.
  4. In Factors, enter Plant-Batch.
  5. Click OK.

Interpret the results

The ANOVA table indicates that the main effects for plant and shift are statistically significant at the 0.05 significance level. The operator effect is not statistically significant at the 0.05 level. The variance component estimates indicate that the variability attributable to batches, shifts, and plants was 52%, 27%, and 18%, respectively, of the total variability.

Nested ANOVA: Temp versus Plant, Operator, Shift, Batch

Analysis of Variance for Temp Source DF SS MS F P Plant 3 731.5156 243.8385 5.854 0.011 Operator 12 499.8125 41.6510 1.303 0.248 Shift 48 1534.9167 31.9774 2.578 0.000 Batch 128 1588.0000 12.4062 Total 191 4354.2448
Variance Components % of Source Var Comp. Total StDev Plant 4.212 17.59 2.052 Operator 0.806 3.37 0.898 Shift 6.524 27.24 2.554 Batch 12.406 51.80 3.522 Total 23.948 4.894
Expected Mean Squares 1 Plant 1.00(4) + 3.00(3) + 12.00(2) + 48.00(1) 2 Operator 1.00(4) + 3.00(3) + 12.00(2) 3 Shift 1.00(4) + 3.00(3) 4 Batch 1.00(4)
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